Stochastic input data brings aleatoric and epistemic uncertainty to the rack seismic analysis. From the synthetic acceleration-time history of the earthquake to the heterogeneous features of the rack system, several sources of uncertainty exist. The manufacturing process itself may produce slight deviations in the dynamic properties and mass distribution of the rack units. Moreover, each unit is loaded with a different number of fuel elements according to the operation needs of the plant. Even the exact clearance spaces between units are hardly inspectable due to radioactive ambiance. Hence, all of these uncertainties propagate across the nonlinear transient analysis and affect the accuracy and robustness of the numerical outputs. This paper carries out a ‘one-factor-ata-time’ parametric analysis of five key input variables: acceleration time-history, rack mass, fuel loading, rack Eigen-frequencies and hydrodynamic masses. This technique examines the impact on the main transient outputs when an analysis parameter is systematically varied while the others remain at their nominal value. Numerical results are provided for a simple two-rack system as a source of insight into the uncertain seismic response of a real rack system. It is highlighted that the dispersion is much higher for the sliding displacements than for the maximal forces on support.

1. Reducing Uncertainty in Structural Safety
Special Session SS6
Ghent, Belgium
28-31 October 2018

2. Alberto Gonzalez, Luis Costas and Arturo
González
Impact of input variables on
the seismic response of free-
standing spent fuel racks

3. Outline
• Free-standing Spent Fuel Storage Racks
• Current seismic analysis methodology
• Uncertain variables
• OFAT parametric analysis of the input variables
• Conclusions (I)
• Analysis of the Coefficients of Variation
• Conclusions (II)

4. Free-standing Spent Fuel Racks
Metallic structures designed to store spent fuel removed from the nuclear
power reactor. Several units are installed together.
• Slightly spaced by only a few centimeters,
• free-standing conditions,
• submerged in water.
Spent Fuel Pool
6x4 racks
Fuel storage
rack unit
~4m
~12m
Nuclear Fuel
assemblies

5. RACK
SYSTEM
STRUCTURAL
MODEL
SEISMIC MODEL
Soler, A.I., & Singh,
K.O. (1982)
FLUID MODEL
Loads and displacements to
• Calculate local stresses
• Check instabilities
SHELL63
MASS21
Current analysis methodology

6. Uncertain variables
A. Data Input
• Acceleration time-history
• Rack mass & weight
• Fuel mass & weight
• Rack Eigen frequencies
• Hydrodynamic mass
matrix
B. Modelling properties
• FE mesh discretization
• Rack-Pool friction
coefficient
• Rack-Pool contact stiffness
• Fuel-Cell contact stiffness
• Fuel-Cell gap
• Fuel flexural rigidity
C. Solution controls
Time marching (‘DELTIM’)
Equilibrium iterations
(‘NEQIT’)
Convergence criteria
(‘CNVTOL’)
Integration parameter
(‘TINTP’)
Mass proportional damping
(‘BETAD’)
Stiffness proportional
damping (‘ALPHAD’)

7. Acceleration time-history

8. Acceleration time-history

9. Rack mass

10. Rack mass

11. Fuel mass

12. Fuel mass

13. Inertia of the rack body beam

14. Inertia of the rack body beam

15. Hydrodynamic added masses

16. Hydrodynamic added masses

17. Conclusions (I)
Variable
Sliding
amplitude
Reaction
forces
Comments
Amplitude of the
seismic loading
Unclear Increase Strong accelerations cause rack
rocking
Rack mass None Decrease Heavy racks are more stable
Fuel mass Unclear Increase Heavy loadings contribute to the
rattling energy
Rigidity of the rack
body beam
Larger Potential
resonance
Determines the energy exchanges
between the fuel ratting and the rack
supports
Hydrodynamic
masses
Unclear Unclear Coupling action that affects the
overall motion

18. Coefficient of
Variation (CV)
CV for a 10% variation in the variables
𝐶𝑉 =
𝜎
𝜇
CV for a 5% variation in the variables

19. Coefficient of
Variation (CV)
CV for a 10% variation in the variables
𝐶𝑉 =
𝜎
𝜇
CV for a 3% variation in the variables

20. Conclusions (II)
• Dispersion is much higher for the sliding displacements (CVs up to 0.8)
than for the maximal forces on support (CVs under 0.2).
• No dependency is observed between the sampling of the input
variables an the resulting Coefficients of Variation.

21. The TRUSS ITN project (http://trussitn.eu) has
received funding from the European Union’s
Horizon 2020 research and innovation
programme under the Marie Skłodowska-Curie
grant agreement No. 642453
Thanks for your attention